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If one candidate is only in two cells in a group (row, column or 3x3 box),
we call it a conjugate pair.
In the example above,
the candidates 8 are in Row 2, only located in Column 3 & 9.
This two (R2C3 & R2C9) are a conjugate pair.
One of those two has to be false (cannot be 8) and the other has to be true (must be 8).
We mark them with two different colors. R2C9
builds another conjugate pair with R1C7,
and R1C7 with R7C7.
We now know that either R2C3 or R7C7 has to be true
(different colors).
Therefore the candidates 8 in the highlighted (yellow) cells can safely be excluded from this cell.
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In the example above, we start with R5C1 and look for candidates 9 which has
a conjugate relationship to R5C8, R8C1 and R6C2 .
By filling the grid, we see that both R5C8 and R6C9 (which
are in the same box) has the same color.
Since every 3x3 box can only have one 9, this color must be the false value.
The candidates 9 can be removed from all cells with this color.
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